Non-uniform torsional eigenmodes of FGM beams

Abstract

In this contribution, which is an extension of our research (Murin et al. in J Eng Struct 175:912-925, 2018 [6]), the influence of spatially varying material properties on torsional eigenvibration of the FGM beams is investigated. Based on the semi-analytical solution of the fourth-order differential equation for non-uniform torsion, the local finite element equations of the twisted FGM beam are established, considering the non-uniform torsion with the effect of warping and secondary deformations due to the angle of twist. The warping part of the first derivative of the twist angle caused by the bimoment is considered as an additional degree of freedom at the beam nodes. The focus of the numerical investigation, with consideration of the warping and Deformation Effect due to the Secondary Torsional Moment (STMDE), is on modal analysis of straight cantilever FGMbeamswith doubly symmetric closed cross-sections. The influence of the spatial variation of the material properties on the eigenfrequencies is investigated. The obtained results are compared with the ones calculated by a very fine mesh of standard solid finite elements.